Blow-up phenomena and peakons for the b-family of FORQ/MCH equations |
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| Authors: | Shaojie Yang Zhijun Qiao Tianzhou Xu |
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| Institution: | 1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China;2. School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA |
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| Abstract: | This paper is devoted to studying the modified b-family of equations with cubic nonlinearity, called the b-family of FORQ/MCH equations, which includes the cubic Camassa–Holm equation (also called Fokas–Olver–Rosenau–Qiao equation) as a special case. We first study the local well-posedness for the Cauchy problem of the equation, and then make good use of fine structure of the equation, we derive the precise blow-up scenario and a new blow-up result with respect to initial data. Finally, peakon solutions are derived. |
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| Keywords: | Local well-posedness Blow-up Peakons |
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